for every \(x\in D^k\) , \(y\in B_r(x)\)  for some \(r>0\) , for some nonnegative \(h \in {H}^{k-1,p}([0,T],D;U)\)  and \(0\leqslant \psi (t)\in L^{\infty }([0,T])\)  and some \(\widetilde{h}\in {H}^{k,p}([0,T],D;U)\) . (Note that the term \(\widetilde{h}\)  was not present in [1]}, but one can generalize the results of that paper to include such a term.)
